Have you tried contacting your local council and asking if they do a scheme which would allow you to apply to go on the waiting list in Doncaster? I moved from Lancashire to Hull in 1998 by doing this,all I had to do was prove that I had either family ties to Hull which I did.I was offered a house in Hull within 6 months.
with the connection,Id have thought everyone in a council house in Doncaster would jump at the chance of moving to the beautiful historic city of York of both places being a home to horse racing